Answer:
x² = 81 , x = ± 9
x² - 18x = 7 : x = 9 ± √(22)
Step-by-step explanation:
x² = 81
simply take the square root of both sides
x = ± 9
x² - 18x = 7
This question is a bit more complicated as there is a variable with a power as well as a variable with no power. To solve for x we are going to have to put the equation in quadratic form then solve using the quadratic equation
x² - 18x = 7
put the equation in quadratic form by subtracting 7 from both sides so that the equation is equal to 0
x² - 18x - 7 = 0
we can now solve for x using the quadratic equation
recall the quadratic equation : [tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]
where the value of a,b and c are derived from the equation
remember the equation is in quadratic form ax² + bx + c = 0
so ax² + bx + c = 0 : x² - 18x - 7 = 0
knowing this we can assign variables, a = 1 , b = -18 and c = -7
now we plug in the variables into the quadratic equation
recall equation : [tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]
a = 1 , b = -18 and c = -7
plug in values
[tex]x=\frac{-(-18)+\sqrt{(-18)^2-4(1)(-7)} }{2(1)}[/tex]
remove parenthesis
[tex]x=\frac{18+\sqrt{(-18)^2-4(1)(-7)} }{2(1)}[/tex]
simplify exponent
[tex]x=\frac{18+\sqrt{324-4(1)(-7)} }{2(1)}[/tex]
simplify multiplication in square root and on denominator
[tex]x=\frac{18+\sqrt{324+28} }{2}[/tex]
simplify addition
[tex]x=\frac{18+\sqrt{352} }{2}[/tex]
simplify radical
[tex]x=\frac{18+4\sqrt{22} }{2}[/tex]
simplify fraction
[tex]x=9+or-\sqrt{22}[/tex]
and we are done!
